I am aware of how to implement the Newton's method for minimization for a smooth analytic function.
I am also aware of log-barrier for constraint minimization.
Now, I am looking to solve the the minimization of L-2 norm with L-1 regularization. Thus, I want to solve,
$$ \text{minimize}_\beta \ ||\textbf{y}-\textbf{X}\beta||_2 $$ $$ \text{subject to} \ ||\beta||_1 \le T $$
$\beta \in R^p$, $X \in R^{n \times p}$. T is a known constant. How do I incoperate the L-1 norm in constraint minimization.